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A note on certain ergodicity coeflcients

Francesco Tudisco — 2015

Special Matrices

We investigate two ergodicity coefficients ɸ ∥∥ and τn−1, originally introduced to bound the subdominant eigenvalues of nonnegative matrices. The former has been generalized to complex matrices in recent years and several properties for such generalized version have been shown so far.We provide a further result concerning the limit of its powers. Then we propose a generalization of the second coefficient τ n−1 and we show that, under mild conditions, it can be used to recast the eigenvector problem...

Localization of dominant eigenpairs and planted communities by means of Frobenius inner products

Dario Fasino;  Francesco Tudisco — 2016

Czechoslovak Mathematical Journal

We propose a new localization result for the leading eigenvalue and eigenvector of a symmetric matrix A . The result exploits the Frobenius inner product between A and a given rank-one landmark matrix X . Different choices for X may be used, depending on the problem under investigation. In particular, we show that the choice where X is the all-ones matrix allows to estimate the signature of the leading eigenvector of A , generalizing previous results on Perron-Frobenius properties of matrices with...

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